Solutions Manual for Fundamental Concepts in the Design of Experiments

Fundamental Concepts in the Design of Experiments, 5e offers comprehensive coverage of the key elements of experimental design used by applied researchers to solve problems in the field. Wide-ranging and accessible, it shows students how to use applied statistics for planning, running, andanalyzing experiments. Featuring over 350 problems taken from the authors' actual industrial consulting experiences, the text gives students valuable practice with real data and problem solving. The problems emphasize the basic philosophy of design and are simple enough for students with limitedmathematical backgrounds to understand. The authors provide extensive coverage of the analysis of residuals, the concept of resolution in fractional replications, Plackett-Burman designs, and Taguchi techniques. SAS (Statistical Analysis System) computer programs are incorporated to facilitateanalysis. Thoroughly revised and updated, this new edition includes sixty new problems, focuses more on computer use (adding computer outputs from statistical packages like Minitab, SPSS, and JMP), and emphasizes graphical procedures including residual plots and normal quantile plots. Ideal for variousadvanced undergraduate and graduate experimental methods courses taught in statistics, engineering, and mathematics departments, this book will also appeal to professionals and researchers doing experimental work.

Preface1. The Experiment, the Design, and the Analysis1.1. Introduction to Experimental Design1.2. The Experiment1.3. The Design1.4. The Analysis1.5. Examples1.6. Summary in Outline1.7. Further ReadingProblems2. Review of Statistical Inference2.1. Introduction2.2. Estimation2.3. Tests of Hypothesis2.4. The Operating Characteristic Curve2.5. How Large a Sample?2.6. Application to Tests on Variances2.7. Application to Tests on Means2.8. Assessing Normality2.9. Applications to Tests on Proportions2.10. Analysis of Experiments with SAS2.11. Further ReadingProblems3. Single-Factor Experiments with No Restrictions on Randomization3.1. Introduction3.2. Analysis of Variance Rationale3.3. After ANOVA--What?3.4. Tests on Means3.5. Confidence Limits on Means3.6. Components of Variance3.7. Checking the Model3.8. SAS Programs for ANOVA and Tests after ANOVA3.9. Summary3.10. Further ReadingProblems4. Single-Factor Experiments: Randomized Block and Latin Square Designs4.1. Introduction4.2. Randomized Complete Block Design4.3. ANOVA Rationale4.4. Missing Values4.5. Latin Squares4.6. Interpretations4.7. Assessing the Model4.8. Graeco-Latin Squares4.9. Extensions4.10. SAS Programs for Randomized Blocks and Latin Squares4.11. Summary4.12. Further ReadingProblems5. Factorial Experiments5.1. Introduction5.2. Factorial Experiments: An Example5.3. Interpretations5.4. The Model and Its Assessment5.5. ANOVA Rationale5.6. One Observation Per Treatment5.7. SAS Programs for Factorial Experiments5.8. Summary5.9. Further ReadingProblems6. Fixed, Random, and Mixed Models6.1. Introduction6.2. Single-Factor Models6.3. Two-Factor Models6.4. EMS Rules6.5. EMS Derivations6.6. The Pseudo-F Test6.7. Expected Mean Squares Via Statistical Computing Packages6.8. Remarks6.9. Repeatability and Reproducibility for a Measurement System6.10. SAS Problems for Random and Mixed Models6.11. Further ReadingProblems7. Nested and Nested-Factorial Experiments7.1. Introduction7.2. Nested Experiments7.3. ANOVA Rationale7.4. Nested-Factorial Experiments7.5. Repeated-Measures Design and Nested-Factorial Experiments7.6. SAS Programs for Nested and Nested-Factorial Experiments7.7. SummaryFurther ReadingProblems8. Experiments of Two or More Factors: Restrictions on Randomization8.1. Introduction8.2. Factorial Experiment in a Randomized Block Design8.3. Factorial Experiment in a Latin Square Design8.4. Remarks8.5. SAS Programs8.6. SummaryProblems9. 2f Factorial Experiments. 9.1. Introduction9.2. 2 Squared Factorial9.3. 2 Cubed Factorial9.4. 2f Remarks9.5. The Yates Method9.6. Analysis of 2f Factorials When n=19.7 Some Commments about Computer Use. 9.8. Summary9.9. Further ReadingProblems10. 3f Factorial Experiments10.1. Introduction10.2. 3 Squared Factorial10.3. 3 Cubed Factorial10.4. Computer Programs10.5. SummaryProblems11. Factorial Experiment: Split-Plot Design11.1. Introduction11.2. A Split-Plot Design11.3. A Split-Split-Plot Design11.4. Using SAS to Analyze a Split-Plot Experiment11.5. Summary11.6. Further ReadingProblems12. Factorial Experiment: Confounding in Blocks12.1. Introduction12.2. Confounding Systems12.3. Block Confounding, No Replication12.4. Block Confounding with Replication12.5. Confounding in 3F Factorials12.6. SAS Progrms12.7. Summary12.8. Further ReadingProblems13. Fractional Replication13.1. Introduction13.2. Aliases13.3. 2f Fractional Replications13.4. Plackett-Burman Designs13.5. Design Resolution13.6. 3f-k Fractional Factorials13.7. SAS Programs13.8. Summary13.9. Further ReadingProblems14. The Taguchi Approach to the Design of Experiments14.1. Introduction14.2. The L4 (2 Cubed) Orthogonal Array14.3. Outer Arrays14.4. Signal-To-Noise Ratio14.5. The L8 (2 7) Orthogonal Array14.6. The L16 (2 15) Orthogonal Array14.7. The L9 (3 4) Orthogonal Array14.8. Some Other Taguchi Designs14.9. Summary14.10. Further ReadingProblems15. Regression15.1. Introduction15.2. Linear Regression15.3. Curvilinear Regression15.4. Orthogonal Polynomials15.5. Multiple Regression15.6. Summa